Person must do an adjustment of status while filing for the green card.
Asylum
-- Asylum seeker can adjust his / her status without going back to home country (person can't go to home country) if he/she granted asylum So this is one exception.
Marriage Based
If spouse is Citizen
-- Any unlawful presence / out of status would be forgiven and the person will be able to adjust his / her status in USA.
If spouse is Green Card Holder
--- The person must go back and appear for an interview. As per the current rule, that person can not apply for any waiver (extreme difficulties - financial / medical) either . However, currently there is a proposal to grant a waiver for the spouse of green card holder. (http://www.uscis.gov/news/alerts/uscis-seeks-comments-proposed-expansion-eligibility-provisional-unlawful-presence-waivers)
Employment Based
--- The person must go back and appear for an interview
I know, you might not like it, but if none of the exception applies to you, then most probably , you will not be able to adjust your status means no Green card. Most likely, your change of status might be denied because of your unlawful presence / out of status (it counts even if it is just one day).
if you want to know more about it please read it here. above information is extracted from this document
http://www.uscis.gov/sites/default/files/USCIS/Laws/Memoranda/Static_Files_Memoranda/2009/revision_redesign_AFM.PDF
This is not a lawyer advice. this is just an opinion. Please consult a lawyer if you want to know more.
Good Luck.